Some of the problem may relate to running the TV as a monitor, I know that when I switch from my monitor to my TV (both are 1920 by 1080) some of the image is cut off on the TV while it's still visible on the monitor.
The refresh rate should be at 60 Hz, I didn't know that anything had a 30 Hz refresh rate.
1280 by 720 is the normal pixel size on a 720 TV, so that's what your video output should be set to, that would be very low resolution for a 32" monitor (normal would be 2560 x 1440) can't imagine that it wouldn't look pretty fuzzy.
If you are changing the pixel size in the Display Settingsl and you aren't seeing a change then something isn't working.
Check to see if your video card has a settings panel, to change the display...